Our framework does not rely on the specific properties of the underlying metric space. Thus, for special metrics, such as Euclidean spaces, or shortest-path metrics induced by sparse graph classes, for which FPT \((1+\epsilon )\) -approximations are known for \(k\) -Median, our framework implies matching approximation for \(k\) -MedianOut. Finally, our framework is quite versatile in that one can extend it to obtain approximation-preserving FPT reductions for related clustering with outliers problems, such as \(k\) -MeansOut, and clustering problems with fair outliers (such as [1]}, [2]}), and Matroid Median with Outliers. We conclude by giving a partial list of the corollaries of our reduction framework. The running time of each algorithm is \(f(k, m, \epsilon ) \cdot n^{O(1)}\)  for some function \(f\)  that depends on the problem and the setting. Next to each result, we also cite the result that we use as a black box to solve the outlier-free clustering problem.
